CONTENTS
1 THE TENSILE TEST  1
1.1 Introduction  1
1.2 Engineering stress and strain  2
1.3 Analysis of the engineering stress-strain curve  3
1.4 True stress and strain  7
1.5 Maximum load  10
1.6 Empirical stress-strain relations  11
1.7 SAMPLE PROBLEM 1  14
1.8 PROPOSED PROBLEMS  15
2 UNIAXIAL STRESS STATE  17
2.1 Introduction  17
2.2 The compression test  17
2.3 The Bauschinger effect  19
2.4 SAMPLE PROBLEM 2  22
2.5 PROPOSED PROBLEMS  23
3 THE YIELD CRITERION FOR METALLIC MATERIALS  25
3.1 Introduction  25
3.2 The yield criterion  25
3.3 Isotropic material  26
3.4 Yield criterion for metals and alloys  27
3.5 Geometrical representation  28
3.6 Tresca’s and von Mises’ criteria  31
3.7 SAMPLE PROBLEM 3  37
3.8 PROPOSED PROBLEMS 38
4 YIELD CRITERION FOR NON-METALLIC MATERIALS  39
4.1 Introduction  39
4.2 Intrinsic curve  40
4.3 Coulomb’s criterion  41
4.4 Drucker-Prager’s yield criterion  43
4.5 Strain hardening  44
4.6 Anisotropic materials  51
4.7 SAMPLE PROBLEM 4  53
4.8 SAMPLE PROBLEM 5  54
4.9 PROPOSED PROBLEMS  55
5 STRESS –STRAIN RELATIONS  57
5.1 Introduction  57
5.2 Prandtl-Reuss equations  60
5.3 Levy-Mises equations  62
5.4 Total strain theory  63
5.5 Validity of Total Strain Theory  68
5.6 SAMPLE PROBLEM 6  69
5.7 SAMPLE PROBLEM 7  70
5.8 PROPOSED PROBLEMS  71
6 PURE BENDING  73
6.1 Introduction  73
6.2 Analysis of the behaviour of a slice  74
6.3 Elastic behaviour  76
6.4 Yielding  78
6.5 SAMPLE PROBLEM 8  83
6.6 SAMPLE PROBLEM 9  84
6.7 PROPOSED PROBLEMS  85
7 ELASTIC-PLASTIC BENDING OF BEAMS  87
7.1 Introduction  87
7.2 Isostatic beams  88
7.3 Hyperstatic beams  91
7.4 Continuous beams  94
7.5 Collapse load computation using the virtual work method  96
7.6 PROPOSED PROBLEMS  101
8 ELASTIC PLASTIC BEHAVIOUR OF PLATES 103
8.1 Introduction  103
8.2 The yield line theory  103
8.3 Application of the principle of virtual work 105
8.4 SAMPLE PROBLEM 10  112
8.5 PROPOSED PROBLEMS  113
9 ELASTIC PLASTIC BEHAVIOUR OF TUBES  115
9.1 Introduction  115
9.2 Thin walled tubes  115
9.3 Strains of the thin walled tube in plastic state  119
9.4 Tube with free ends 120
9.5 Tube with closed ends  121
9.6 Maximum pressure  122
9.7 Thick-walled tubes  125
9.8 SAMPLE PROBLEM 11  133
9.9 PROPOSED PROBLEMS  134
10 VISCOPLASTICITY  135
10.1 Introduction  135
10.2 Definitions  135
10.3 Creep behaviour of materials  137
10.4 Creep at low temperatures (logarithmic creep)  139
10.5 Creep at high temperatures  140
10.6 Andrade’s creep law  141
10.7 Dependence of creep strain rate on stress and temperature  141
10.8 Creep under multiaxial stress states  142
10.9 Stress relaxation  144
10.10 SAMPLE PROBLEM 12  146
10.11 PROPOSED PROBLEMS  147

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